1 Data preparation

1.1 Outline

  • Load scripts: loads libraries and useful scripts used in the analyses; all .R files contained in scripts at the root of the factory are automatically loaded

  • Load data: imports datasets, and may contain some ad hoc changes to the data such as specific data cleaning (not used in other reports), new variables used in the analyses, etc.

1.2 Load packages


library(reportfactory)
library(here)
library(rio) 
library(tidyverse)
library(incidence)
library(distcrete)
library(epitrix)
library(earlyR)
library(projections)
library(linelist)
library(remotes)
library(janitor)
library(kableExtra)
library(DT)
library(cyphr)
library(chngpt)
library(lubridate)
library(ggpubr)
library(ggnewscale)

1.3 Load scripts

These scripts will load:

  • all scripts stored as .R files inside /scripts/
  • all scripts stored as .R files inside /src/

These scripts also contain routines to access the latest clean encrypted data (see next section).


reportfactory::rfh_load_scripts()

1.4 Load clean data

We import the latest NHS pathways data:


x <- import_pathways() %>%
  as_tibble()
x
## # A tibble: 148,423 x 11
##    site_type date       sex   age   ccg_code ccg_name count postcode nhs_region
##    <chr>     <date>     <chr> <chr> <chr>    <chr>    <int> <chr>    <chr>     
##  1 111       2020-03-18 fema… 0-18  e380000… nhs_bar…    35 rm13ae   London    
##  2 111       2020-03-18 fema… 0-18  e380000… nhs_bed…    27 mk454hr  East of E…
##  3 111       2020-03-18 fema… 0-18  e380000… nhs_bla…     9 bb12fd   North West
##  4 111       2020-03-18 fema… 0-18  e380000… nhs_bro…    11 br33ql   London    
##  5 111       2020-03-18 fema… 0-18  e380000… nhs_can…     9 ws111jp  Midlands  
##  6 111       2020-03-18 fema… 0-18  e380000… nhs_cit…    12 n15lz    London    
##  7 111       2020-03-18 fema… 0-18  e380000… nhs_enf…     7 en40dy   London    
##  8 111       2020-03-18 fema… 0-18  e380000… nhs_ham…     6 dl62uu   North Eas…
##  9 111       2020-03-18 fema… 0-18  e380000… nhs_har…    24 ts232la  North Eas…
## 10 111       2020-03-18 fema… 0-18  e380000… nhs_kin…     6 kt11eu   London    
## # … with 148,413 more rows, and 2 more variables: day <int>, weekday <fct>

We also import demographics data for NHS regions in England, used later in our analysis:


path <- here::here("data", "csv", "nhs_region_population_2018.csv")
nhs_region_pop <- rio::import(path) %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

nhs_region_pop$nhs_region <- gsub(" Of ", " of ", nhs_region_pop$nhs_region)
nhs_region_pop$nhs_region <- gsub(" And ", " and ", nhs_region_pop$nhs_region)
nhs_region_pop
##                  nhs_region variable      value
## 1                North West     0-18 0.22538599
## 2  North East and Yorkshire     0-18 0.21876449
## 3                  Midlands     0-18 0.22564656
## 4           East of England     0-18 0.22810783
## 5                    London     0-18 0.23764782
## 6                South East     0-18 0.22458811
## 7                South West     0-18 0.20799797
## 8                North West    19-69 0.64274078
## 9  North East and Yorkshire    19-69 0.64437753
## 10                 Midlands    19-69 0.63876675
## 11          East of England    19-69 0.63034229
## 12                   London    19-69 0.67820084
## 13               South East    19-69 0.63267336
## 14               South West    19-69 0.63176131
## 15               North West   70-120 0.13187323
## 16 North East and Yorkshire   70-120 0.13685797
## 17                 Midlands   70-120 0.13558669
## 18          East of England   70-120 0.14154988
## 19                   London   70-120 0.08415135
## 20               South East   70-120 0.14273853
## 21               South West   70-120 0.16024072

Finally, we import publically available deaths per NHS region:


dth <- import_deaths() %>%
  mutate(nhs_region = str_to_title(gsub("_"," ",nhs_region)))

#truncation to account for reporting delay
delay_max <- 21

dth$nhs_region <- gsub(" Of ", " of ", dth$nhs_region)
dth$nhs_region <- gsub(" And ", " and ", dth$nhs_region)
dth
##     date_report               nhs_region deaths
## 1    2020-03-01          East of England      0
## 2    2020-03-02          East of England      1
## 3    2020-03-03          East of England      0
## 4    2020-03-04          East of England      0
## 5    2020-03-05          East of England      0
## 6    2020-03-06          East of England      1
## 7    2020-03-07          East of England      0
## 8    2020-03-08          East of England      0
## 9    2020-03-09          East of England      1
## 10   2020-03-10          East of England      0
## 11   2020-03-11          East of England      0
## 12   2020-03-12          East of England      0
## 13   2020-03-13          East of England      1
## 14   2020-03-14          East of England      2
## 15   2020-03-15          East of England      2
## 16   2020-03-16          East of England      1
## 17   2020-03-17          East of England      1
## 18   2020-03-18          East of England      5
## 19   2020-03-19          East of England      4
## 20   2020-03-20          East of England      2
## 21   2020-03-21          East of England     11
## 22   2020-03-22          East of England     12
## 23   2020-03-23          East of England     11
## 24   2020-03-24          East of England     19
## 25   2020-03-25          East of England     26
## 26   2020-03-26          East of England     36
## 27   2020-03-27          East of England     38
## 28   2020-03-28          East of England     28
## 29   2020-03-29          East of England     43
## 30   2020-03-30          East of England     45
## 31   2020-03-31          East of England     70
## 32   2020-04-01          East of England     62
## 33   2020-04-02          East of England     64
## 34   2020-04-03          East of England     80
## 35   2020-04-04          East of England     71
## 36   2020-04-05          East of England     76
## 37   2020-04-06          East of England     71
## 38   2020-04-07          East of England     93
## 39   2020-04-08          East of England    111
## 40   2020-04-09          East of England     87
## 41   2020-04-10          East of England     74
## 42   2020-04-11          East of England     91
## 43   2020-04-12          East of England    101
## 44   2020-04-13          East of England     78
## 45   2020-04-14          East of England     61
## 46   2020-04-15          East of England     82
## 47   2020-04-16          East of England     74
## 48   2020-04-17          East of England     86
## 49   2020-04-18          East of England     64
## 50   2020-04-19          East of England     67
## 51   2020-04-20          East of England     67
## 52   2020-04-21          East of England     75
## 53   2020-04-22          East of England     67
## 54   2020-04-23          East of England     49
## 55   2020-04-24          East of England     66
## 56   2020-04-25          East of England     54
## 57   2020-04-26          East of England     48
## 58   2020-04-27          East of England     46
## 59   2020-04-28          East of England     58
## 60   2020-04-29          East of England     32
## 61   2020-04-30          East of England     45
## 62   2020-05-01          East of England     49
## 63   2020-05-02          East of England     29
## 64   2020-05-03          East of England     41
## 65   2020-05-04          East of England     19
## 66   2020-05-05          East of England     36
## 67   2020-05-06          East of England     30
## 68   2020-05-07          East of England     33
## 69   2020-05-08          East of England     33
## 70   2020-05-09          East of England     29
## 71   2020-05-10          East of England     22
## 72   2020-05-11          East of England     18
## 73   2020-05-12          East of England     21
## 74   2020-05-13          East of England     27
## 75   2020-05-14          East of England     26
## 76   2020-05-15          East of England     19
## 77   2020-05-16          East of England     26
## 78   2020-05-17          East of England     17
## 79   2020-05-18          East of England     25
## 80   2020-05-19          East of England     15
## 81   2020-05-20          East of England     26
## 82   2020-05-21          East of England     21
## 83   2020-05-22          East of England     13
## 84   2020-05-23          East of England     12
## 85   2020-05-24          East of England     17
## 86   2020-05-25          East of England     25
## 87   2020-05-26          East of England     14
## 88   2020-05-27          East of England     12
## 89   2020-05-28          East of England     17
## 90   2020-05-29          East of England     16
## 91   2020-05-30          East of England      9
## 92   2020-05-31          East of England      8
## 93   2020-06-01          East of England     17
## 94   2020-06-02          East of England     14
## 95   2020-06-03          East of England     10
## 96   2020-06-04          East of England      7
## 97   2020-06-05          East of England     12
## 98   2020-06-06          East of England      5
## 99   2020-06-07          East of England      9
## 100  2020-06-08          East of England      5
## 101  2020-06-09          East of England      6
## 102  2020-06-10          East of England      8
## 103  2020-06-11          East of England      0
## 104  2020-06-12          East of England      7
## 105  2020-06-13          East of England      2
## 106  2020-06-14          East of England      2
## 107  2020-06-15          East of England      2
## 108  2020-03-01                   London      0
## 109  2020-03-02                   London      0
## 110  2020-03-03                   London      0
## 111  2020-03-04                   London      0
## 112  2020-03-05                   London      0
## 113  2020-03-06                   London      1
## 114  2020-03-07                   London      1
## 115  2020-03-08                   London      0
## 116  2020-03-09                   London      1
## 117  2020-03-10                   London      0
## 118  2020-03-11                   London      7
## 119  2020-03-12                   London      6
## 120  2020-03-13                   London     10
## 121  2020-03-14                   London     14
## 122  2020-03-15                   London     10
## 123  2020-03-16                   London     18
## 124  2020-03-17                   London     25
## 125  2020-03-18                   London     31
## 126  2020-03-19                   London     25
## 127  2020-03-20                   London     44
## 128  2020-03-21                   London     50
## 129  2020-03-22                   London     54
## 130  2020-03-23                   London     64
## 131  2020-03-24                   London     87
## 132  2020-03-25                   London    113
## 133  2020-03-26                   London    130
## 134  2020-03-27                   London    130
## 135  2020-03-28                   London    122
## 136  2020-03-29                   London    147
## 137  2020-03-30                   London    150
## 138  2020-03-31                   London    181
## 139  2020-04-01                   London    202
## 140  2020-04-02                   London    190
## 141  2020-04-03                   London    196
## 142  2020-04-04                   London    230
## 143  2020-04-05                   London    195
## 144  2020-04-06                   London    197
## 145  2020-04-07                   London    220
## 146  2020-04-08                   London    238
## 147  2020-04-09                   London    206
## 148  2020-04-10                   London    170
## 149  2020-04-11                   London    177
## 150  2020-04-12                   London    158
## 151  2020-04-13                   London    166
## 152  2020-04-14                   London    144
## 153  2020-04-15                   London    142
## 154  2020-04-16                   London    139
## 155  2020-04-17                   London    100
## 156  2020-04-18                   London    101
## 157  2020-04-19                   London    103
## 158  2020-04-20                   London     95
## 159  2020-04-21                   London     95
## 160  2020-04-22                   London    109
## 161  2020-04-23                   London     77
## 162  2020-04-24                   London     71
## 163  2020-04-25                   London     58
## 164  2020-04-26                   London     53
## 165  2020-04-27                   London     51
## 166  2020-04-28                   London     43
## 167  2020-04-29                   London     44
## 168  2020-04-30                   London     40
## 169  2020-05-01                   London     41
## 170  2020-05-02                   London     40
## 171  2020-05-03                   London     36
## 172  2020-05-04                   London     30
## 173  2020-05-05                   London     25
## 174  2020-05-06                   London     37
## 175  2020-05-07                   London     37
## 176  2020-05-08                   London     29
## 177  2020-05-09                   London     23
## 178  2020-05-10                   London     26
## 179  2020-05-11                   London     18
## 180  2020-05-12                   London     18
## 181  2020-05-13                   London     16
## 182  2020-05-14                   London     20
## 183  2020-05-15                   London     18
## 184  2020-05-16                   London     14
## 185  2020-05-17                   London     15
## 186  2020-05-18                   London      9
## 187  2020-05-19                   London     13
## 188  2020-05-20                   London     19
## 189  2020-05-21                   London     12
## 190  2020-05-22                   London     10
## 191  2020-05-23                   London      6
## 192  2020-05-24                   London      7
## 193  2020-05-25                   London      9
## 194  2020-05-26                   London     12
## 195  2020-05-27                   London      7
## 196  2020-05-28                   London      8
## 197  2020-05-29                   London      7
## 198  2020-05-30                   London     12
## 199  2020-05-31                   London      6
## 200  2020-06-01                   London     10
## 201  2020-06-02                   London      7
## 202  2020-06-03                   London      6
## 203  2020-06-04                   London      8
## 204  2020-06-05                   London      3
## 205  2020-06-06                   London      0
## 206  2020-06-07                   London      4
## 207  2020-06-08                   London      5
## 208  2020-06-09                   London      2
## 209  2020-06-10                   London      7
## 210  2020-06-11                   London      5
## 211  2020-06-12                   London      2
## 212  2020-06-13                   London      3
## 213  2020-06-14                   London      2
## 214  2020-06-15                   London      0
## 215  2020-03-01                 Midlands      0
## 216  2020-03-02                 Midlands      0
## 217  2020-03-03                 Midlands      1
## 218  2020-03-04                 Midlands      0
## 219  2020-03-05                 Midlands      0
## 220  2020-03-06                 Midlands      0
## 221  2020-03-07                 Midlands      0
## 222  2020-03-08                 Midlands      3
## 223  2020-03-09                 Midlands      1
## 224  2020-03-10                 Midlands      0
## 225  2020-03-11                 Midlands      2
## 226  2020-03-12                 Midlands      6
## 227  2020-03-13                 Midlands      5
## 228  2020-03-14                 Midlands      4
## 229  2020-03-15                 Midlands      5
## 230  2020-03-16                 Midlands     11
## 231  2020-03-17                 Midlands      8
## 232  2020-03-18                 Midlands     13
## 233  2020-03-19                 Midlands      8
## 234  2020-03-20                 Midlands     28
## 235  2020-03-21                 Midlands     13
## 236  2020-03-22                 Midlands     31
## 237  2020-03-23                 Midlands     33
## 238  2020-03-24                 Midlands     41
## 239  2020-03-25                 Midlands     48
## 240  2020-03-26                 Midlands     64
## 241  2020-03-27                 Midlands     72
## 242  2020-03-28                 Midlands     89
## 243  2020-03-29                 Midlands     92
## 244  2020-03-30                 Midlands     90
## 245  2020-03-31                 Midlands    123
## 246  2020-04-01                 Midlands    140
## 247  2020-04-02                 Midlands    142
## 248  2020-04-03                 Midlands    124
## 249  2020-04-04                 Midlands    151
## 250  2020-04-05                 Midlands    164
## 251  2020-04-06                 Midlands    140
## 252  2020-04-07                 Midlands    123
## 253  2020-04-08                 Midlands    186
## 254  2020-04-09                 Midlands    139
## 255  2020-04-10                 Midlands    127
## 256  2020-04-11                 Midlands    142
## 257  2020-04-12                 Midlands    139
## 258  2020-04-13                 Midlands    120
## 259  2020-04-14                 Midlands    116
## 260  2020-04-15                 Midlands    147
## 261  2020-04-16                 Midlands    102
## 262  2020-04-17                 Midlands    118
## 263  2020-04-18                 Midlands    115
## 264  2020-04-19                 Midlands     92
## 265  2020-04-20                 Midlands    107
## 266  2020-04-21                 Midlands     86
## 267  2020-04-22                 Midlands     78
## 268  2020-04-23                 Midlands    103
## 269  2020-04-24                 Midlands     79
## 270  2020-04-25                 Midlands     72
## 271  2020-04-26                 Midlands     81
## 272  2020-04-27                 Midlands     74
## 273  2020-04-28                 Midlands     68
## 274  2020-04-29                 Midlands     53
## 275  2020-04-30                 Midlands     56
## 276  2020-05-01                 Midlands     64
## 277  2020-05-02                 Midlands     51
## 278  2020-05-03                 Midlands     52
## 279  2020-05-04                 Midlands     61
## 280  2020-05-05                 Midlands     58
## 281  2020-05-06                 Midlands     59
## 282  2020-05-07                 Midlands     48
## 283  2020-05-08                 Midlands     34
## 284  2020-05-09                 Midlands     37
## 285  2020-05-10                 Midlands     42
## 286  2020-05-11                 Midlands     33
## 287  2020-05-12                 Midlands     45
## 288  2020-05-13                 Midlands     40
## 289  2020-05-14                 Midlands     37
## 290  2020-05-15                 Midlands     40
## 291  2020-05-16                 Midlands     34
## 292  2020-05-17                 Midlands     31
## 293  2020-05-18                 Midlands     34
## 294  2020-05-19                 Midlands     34
## 295  2020-05-20                 Midlands     36
## 296  2020-05-21                 Midlands     32
## 297  2020-05-22                 Midlands     27
## 298  2020-05-23                 Midlands     34
## 299  2020-05-24                 Midlands     19
## 300  2020-05-25                 Midlands     26
## 301  2020-05-26                 Midlands     33
## 302  2020-05-27                 Midlands     29
## 303  2020-05-28                 Midlands     27
## 304  2020-05-29                 Midlands     20
## 305  2020-05-30                 Midlands     20
## 306  2020-05-31                 Midlands     21
## 307  2020-06-01                 Midlands     20
## 308  2020-06-02                 Midlands     22
## 309  2020-06-03                 Midlands     23
## 310  2020-06-04                 Midlands     15
## 311  2020-06-05                 Midlands     21
## 312  2020-06-06                 Midlands     20
## 313  2020-06-07                 Midlands     16
## 314  2020-06-08                 Midlands     15
## 315  2020-06-09                 Midlands     17
## 316  2020-06-10                 Midlands     14
## 317  2020-06-11                 Midlands     13
## 318  2020-06-12                 Midlands      9
## 319  2020-06-13                 Midlands      3
## 320  2020-06-14                 Midlands     12
## 321  2020-06-15                 Midlands      1
## 322  2020-03-01 North East and Yorkshire      0
## 323  2020-03-02 North East and Yorkshire      0
## 324  2020-03-03 North East and Yorkshire      0
## 325  2020-03-04 North East and Yorkshire      0
## 326  2020-03-05 North East and Yorkshire      0
## 327  2020-03-06 North East and Yorkshire      0
## 328  2020-03-07 North East and Yorkshire      0
## 329  2020-03-08 North East and Yorkshire      0
## 330  2020-03-09 North East and Yorkshire      0
## 331  2020-03-10 North East and Yorkshire      0
## 332  2020-03-11 North East and Yorkshire      0
## 333  2020-03-12 North East and Yorkshire      0
## 334  2020-03-13 North East and Yorkshire      0
## 335  2020-03-14 North East and Yorkshire      0
## 336  2020-03-15 North East and Yorkshire      2
## 337  2020-03-16 North East and Yorkshire      3
## 338  2020-03-17 North East and Yorkshire      1
## 339  2020-03-18 North East and Yorkshire      2
## 340  2020-03-19 North East and Yorkshire      6
## 341  2020-03-20 North East and Yorkshire      5
## 342  2020-03-21 North East and Yorkshire      6
## 343  2020-03-22 North East and Yorkshire      7
## 344  2020-03-23 North East and Yorkshire      9
## 345  2020-03-24 North East and Yorkshire      8
## 346  2020-03-25 North East and Yorkshire     18
## 347  2020-03-26 North East and Yorkshire     21
## 348  2020-03-27 North East and Yorkshire     28
## 349  2020-03-28 North East and Yorkshire     35
## 350  2020-03-29 North East and Yorkshire     38
## 351  2020-03-30 North East and Yorkshire     64
## 352  2020-03-31 North East and Yorkshire     60
## 353  2020-04-01 North East and Yorkshire     67
## 354  2020-04-02 North East and Yorkshire     74
## 355  2020-04-03 North East and Yorkshire    100
## 356  2020-04-04 North East and Yorkshire    105
## 357  2020-04-05 North East and Yorkshire     92
## 358  2020-04-06 North East and Yorkshire     96
## 359  2020-04-07 North East and Yorkshire    102
## 360  2020-04-08 North East and Yorkshire    107
## 361  2020-04-09 North East and Yorkshire    111
## 362  2020-04-10 North East and Yorkshire    117
## 363  2020-04-11 North East and Yorkshire     98
## 364  2020-04-12 North East and Yorkshire     84
## 365  2020-04-13 North East and Yorkshire     94
## 366  2020-04-14 North East and Yorkshire    107
## 367  2020-04-15 North East and Yorkshire     96
## 368  2020-04-16 North East and Yorkshire    103
## 369  2020-04-17 North East and Yorkshire     88
## 370  2020-04-18 North East and Yorkshire     95
## 371  2020-04-19 North East and Yorkshire     88
## 372  2020-04-20 North East and Yorkshire    100
## 373  2020-04-21 North East and Yorkshire     76
## 374  2020-04-22 North East and Yorkshire     84
## 375  2020-04-23 North East and Yorkshire     63
## 376  2020-04-24 North East and Yorkshire     72
## 377  2020-04-25 North East and Yorkshire     69
## 378  2020-04-26 North East and Yorkshire     65
## 379  2020-04-27 North East and Yorkshire     65
## 380  2020-04-28 North East and Yorkshire     57
## 381  2020-04-29 North East and Yorkshire     69
## 382  2020-04-30 North East and Yorkshire     57
## 383  2020-05-01 North East and Yorkshire     64
## 384  2020-05-02 North East and Yorkshire     48
## 385  2020-05-03 North East and Yorkshire     40
## 386  2020-05-04 North East and Yorkshire     49
## 387  2020-05-05 North East and Yorkshire     40
## 388  2020-05-06 North East and Yorkshire     50
## 389  2020-05-07 North East and Yorkshire     45
## 390  2020-05-08 North East and Yorkshire     42
## 391  2020-05-09 North East and Yorkshire     44
## 392  2020-05-10 North East and Yorkshire     40
## 393  2020-05-11 North East and Yorkshire     29
## 394  2020-05-12 North East and Yorkshire     27
## 395  2020-05-13 North East and Yorkshire     28
## 396  2020-05-14 North East and Yorkshire     30
## 397  2020-05-15 North East and Yorkshire     32
## 398  2020-05-16 North East and Yorkshire     35
## 399  2020-05-17 North East and Yorkshire     26
## 400  2020-05-18 North East and Yorkshire     29
## 401  2020-05-19 North East and Yorkshire     27
## 402  2020-05-20 North East and Yorkshire     21
## 403  2020-05-21 North East and Yorkshire     33
## 404  2020-05-22 North East and Yorkshire     22
## 405  2020-05-23 North East and Yorkshire     18
## 406  2020-05-24 North East and Yorkshire     25
## 407  2020-05-25 North East and Yorkshire     21
## 408  2020-05-26 North East and Yorkshire     21
## 409  2020-05-27 North East and Yorkshire     22
## 410  2020-05-28 North East and Yorkshire     20
## 411  2020-05-29 North East and Yorkshire     25
## 412  2020-05-30 North East and Yorkshire     20
## 413  2020-05-31 North East and Yorkshire     19
## 414  2020-06-01 North East and Yorkshire     16
## 415  2020-06-02 North East and Yorkshire     22
## 416  2020-06-03 North East and Yorkshire     22
## 417  2020-06-04 North East and Yorkshire     17
## 418  2020-06-05 North East and Yorkshire     17
## 419  2020-06-06 North East and Yorkshire     20
## 420  2020-06-07 North East and Yorkshire     13
## 421  2020-06-08 North East and Yorkshire     11
## 422  2020-06-09 North East and Yorkshire     11
## 423  2020-06-10 North East and Yorkshire     16
## 424  2020-06-11 North East and Yorkshire      6
## 425  2020-06-12 North East and Yorkshire      8
## 426  2020-06-13 North East and Yorkshire      8
## 427  2020-06-14 North East and Yorkshire     11
## 428  2020-06-15 North East and Yorkshire      5
## 429  2020-03-01               North West      0
## 430  2020-03-02               North West      0
## 431  2020-03-03               North West      0
## 432  2020-03-04               North West      0
## 433  2020-03-05               North West      1
## 434  2020-03-06               North West      0
## 435  2020-03-07               North West      0
## 436  2020-03-08               North West      1
## 437  2020-03-09               North West      0
## 438  2020-03-10               North West      0
## 439  2020-03-11               North West      0
## 440  2020-03-12               North West      2
## 441  2020-03-13               North West      3
## 442  2020-03-14               North West      1
## 443  2020-03-15               North West      4
## 444  2020-03-16               North West      2
## 445  2020-03-17               North West      4
## 446  2020-03-18               North West      6
## 447  2020-03-19               North West      7
## 448  2020-03-20               North West     10
## 449  2020-03-21               North West     11
## 450  2020-03-22               North West     13
## 451  2020-03-23               North West     16
## 452  2020-03-24               North West     21
## 453  2020-03-25               North West     21
## 454  2020-03-26               North West     29
## 455  2020-03-27               North West     35
## 456  2020-03-28               North West     28
## 457  2020-03-29               North West     46
## 458  2020-03-30               North West     67
## 459  2020-03-31               North West     52
## 460  2020-04-01               North West     86
## 461  2020-04-02               North West     96
## 462  2020-04-03               North West     95
## 463  2020-04-04               North West     98
## 464  2020-04-05               North West    102
## 465  2020-04-06               North West    100
## 466  2020-04-07               North West    134
## 467  2020-04-08               North West    127
## 468  2020-04-09               North West    119
## 469  2020-04-10               North West    117
## 470  2020-04-11               North West    139
## 471  2020-04-12               North West    126
## 472  2020-04-13               North West    129
## 473  2020-04-14               North West    131
## 474  2020-04-15               North West    114
## 475  2020-04-16               North West    134
## 476  2020-04-17               North West     98
## 477  2020-04-18               North West    113
## 478  2020-04-19               North West     71
## 479  2020-04-20               North West     83
## 480  2020-04-21               North West     76
## 481  2020-04-22               North West     86
## 482  2020-04-23               North West     85
## 483  2020-04-24               North West     66
## 484  2020-04-25               North West     65
## 485  2020-04-26               North West     55
## 486  2020-04-27               North West     54
## 487  2020-04-28               North West     57
## 488  2020-04-29               North West     62
## 489  2020-04-30               North West     59
## 490  2020-05-01               North West     45
## 491  2020-05-02               North West     56
## 492  2020-05-03               North West     55
## 493  2020-05-04               North West     48
## 494  2020-05-05               North West     48
## 495  2020-05-06               North West     44
## 496  2020-05-07               North West     49
## 497  2020-05-08               North West     42
## 498  2020-05-09               North West     30
## 499  2020-05-10               North West     41
## 500  2020-05-11               North West     34
## 501  2020-05-12               North West     38
## 502  2020-05-13               North West     25
## 503  2020-05-14               North West     26
## 504  2020-05-15               North West     33
## 505  2020-05-16               North West     32
## 506  2020-05-17               North West     24
## 507  2020-05-18               North West     31
## 508  2020-05-19               North West     35
## 509  2020-05-20               North West     27
## 510  2020-05-21               North West     26
## 511  2020-05-22               North West     26
## 512  2020-05-23               North West     31
## 513  2020-05-24               North West     26
## 514  2020-05-25               North West     31
## 515  2020-05-26               North West     27
## 516  2020-05-27               North West     27
## 517  2020-05-28               North West     28
## 518  2020-05-29               North West     20
## 519  2020-05-30               North West     17
## 520  2020-05-31               North West     13
## 521  2020-06-01               North West     12
## 522  2020-06-02               North West     27
## 523  2020-06-03               North West     21
## 524  2020-06-04               North West     20
## 525  2020-06-05               North West     15
## 526  2020-06-06               North West     23
## 527  2020-06-07               North West     17
## 528  2020-06-08               North West     19
## 529  2020-06-09               North West     15
## 530  2020-06-10               North West     13
## 531  2020-06-11               North West     14
## 532  2020-06-12               North West      5
## 533  2020-06-13               North West      6
## 534  2020-06-14               North West     11
## 535  2020-06-15               North West      3
## 536  2020-03-01               South East      0
## 537  2020-03-02               South East      0
## 538  2020-03-03               South East      1
## 539  2020-03-04               South East      0
## 540  2020-03-05               South East      1
## 541  2020-03-06               South East      0
## 542  2020-03-07               South East      0
## 543  2020-03-08               South East      1
## 544  2020-03-09               South East      1
## 545  2020-03-10               South East      1
## 546  2020-03-11               South East      1
## 547  2020-03-12               South East      0
## 548  2020-03-13               South East      1
## 549  2020-03-14               South East      1
## 550  2020-03-15               South East      5
## 551  2020-03-16               South East      8
## 552  2020-03-17               South East      7
## 553  2020-03-18               South East     10
## 554  2020-03-19               South East      9
## 555  2020-03-20               South East     14
## 556  2020-03-21               South East      7
## 557  2020-03-22               South East     25
## 558  2020-03-23               South East     20
## 559  2020-03-24               South East     22
## 560  2020-03-25               South East     29
## 561  2020-03-26               South East     35
## 562  2020-03-27               South East     34
## 563  2020-03-28               South East     36
## 564  2020-03-29               South East     54
## 565  2020-03-30               South East     58
## 566  2020-03-31               South East     65
## 567  2020-04-01               South East     66
## 568  2020-04-02               South East     55
## 569  2020-04-03               South East     72
## 570  2020-04-04               South East     80
## 571  2020-04-05               South East     82
## 572  2020-04-06               South East     88
## 573  2020-04-07               South East    100
## 574  2020-04-08               South East     83
## 575  2020-04-09               South East    104
## 576  2020-04-10               South East     88
## 577  2020-04-11               South East     88
## 578  2020-04-12               South East     88
## 579  2020-04-13               South East     84
## 580  2020-04-14               South East     65
## 581  2020-04-15               South East     72
## 582  2020-04-16               South East     56
## 583  2020-04-17               South East     86
## 584  2020-04-18               South East     57
## 585  2020-04-19               South East     70
## 586  2020-04-20               South East     86
## 587  2020-04-21               South East     50
## 588  2020-04-22               South East     54
## 589  2020-04-23               South East     57
## 590  2020-04-24               South East     64
## 591  2020-04-25               South East     51
## 592  2020-04-26               South East     51
## 593  2020-04-27               South East     40
## 594  2020-04-28               South East     40
## 595  2020-04-29               South East     47
## 596  2020-04-30               South East     29
## 597  2020-05-01               South East     37
## 598  2020-05-02               South East     36
## 599  2020-05-03               South East     17
## 600  2020-05-04               South East     35
## 601  2020-05-05               South East     29
## 602  2020-05-06               South East     25
## 603  2020-05-07               South East     27
## 604  2020-05-08               South East     26
## 605  2020-05-09               South East     28
## 606  2020-05-10               South East     19
## 607  2020-05-11               South East     25
## 608  2020-05-12               South East     27
## 609  2020-05-13               South East     18
## 610  2020-05-14               South East     32
## 611  2020-05-15               South East     24
## 612  2020-05-16               South East     22
## 613  2020-05-17               South East     18
## 614  2020-05-18               South East     22
## 615  2020-05-19               South East     12
## 616  2020-05-20               South East     22
## 617  2020-05-21               South East     14
## 618  2020-05-22               South East     17
## 619  2020-05-23               South East     21
## 620  2020-05-24               South East     16
## 621  2020-05-25               South East     13
## 622  2020-05-26               South East     19
## 623  2020-05-27               South East     17
## 624  2020-05-28               South East     12
## 625  2020-05-29               South East     18
## 626  2020-05-30               South East      8
## 627  2020-05-31               South East     10
## 628  2020-06-01               South East     11
## 629  2020-06-02               South East     12
## 630  2020-06-03               South East     17
## 631  2020-06-04               South East     11
## 632  2020-06-05               South East      9
## 633  2020-06-06               South East      9
## 634  2020-06-07               South East     11
## 635  2020-06-08               South East      5
## 636  2020-06-09               South East      9
## 637  2020-06-10               South East      8
## 638  2020-06-11               South East      3
## 639  2020-06-12               South East      5
## 640  2020-06-13               South East      2
## 641  2020-06-14               South East      5
## 642  2020-06-15               South East      0
## 643  2020-03-01               South West      0
## 644  2020-03-02               South West      0
## 645  2020-03-03               South West      0
## 646  2020-03-04               South West      0
## 647  2020-03-05               South West      0
## 648  2020-03-06               South West      0
## 649  2020-03-07               South West      0
## 650  2020-03-08               South West      0
## 651  2020-03-09               South West      0
## 652  2020-03-10               South West      0
## 653  2020-03-11               South West      1
## 654  2020-03-12               South West      0
## 655  2020-03-13               South West      0
## 656  2020-03-14               South West      1
## 657  2020-03-15               South West      0
## 658  2020-03-16               South West      0
## 659  2020-03-17               South West      2
## 660  2020-03-18               South West      2
## 661  2020-03-19               South West      5
## 662  2020-03-20               South West      3
## 663  2020-03-21               South West      6
## 664  2020-03-22               South West      9
## 665  2020-03-23               South West      9
## 666  2020-03-24               South West      7
## 667  2020-03-25               South West      9
## 668  2020-03-26               South West     11
## 669  2020-03-27               South West     13
## 670  2020-03-28               South West     21
## 671  2020-03-29               South West     18
## 672  2020-03-30               South West     23
## 673  2020-03-31               South West     23
## 674  2020-04-01               South West     22
## 675  2020-04-02               South West     23
## 676  2020-04-03               South West     30
## 677  2020-04-04               South West     42
## 678  2020-04-05               South West     32
## 679  2020-04-06               South West     34
## 680  2020-04-07               South West     39
## 681  2020-04-08               South West     47
## 682  2020-04-09               South West     24
## 683  2020-04-10               South West     46
## 684  2020-04-11               South West     43
## 685  2020-04-12               South West     23
## 686  2020-04-13               South West     27
## 687  2020-04-14               South West     24
## 688  2020-04-15               South West     32
## 689  2020-04-16               South West     29
## 690  2020-04-17               South West     33
## 691  2020-04-18               South West     25
## 692  2020-04-19               South West     31
## 693  2020-04-20               South West     26
## 694  2020-04-21               South West     26
## 695  2020-04-22               South West     23
## 696  2020-04-23               South West     17
## 697  2020-04-24               South West     19
## 698  2020-04-25               South West     15
## 699  2020-04-26               South West     27
## 700  2020-04-27               South West     13
## 701  2020-04-28               South West     17
## 702  2020-04-29               South West     15
## 703  2020-04-30               South West     26
## 704  2020-05-01               South West      6
## 705  2020-05-02               South West      7
## 706  2020-05-03               South West     10
## 707  2020-05-04               South West     17
## 708  2020-05-05               South West     14
## 709  2020-05-06               South West     19
## 710  2020-05-07               South West     16
## 711  2020-05-08               South West      6
## 712  2020-05-09               South West     11
## 713  2020-05-10               South West      5
## 714  2020-05-11               South West      8
## 715  2020-05-12               South West      7
## 716  2020-05-13               South West      7
## 717  2020-05-14               South West      6
## 718  2020-05-15               South West      4
## 719  2020-05-16               South West      4
## 720  2020-05-17               South West      6
## 721  2020-05-18               South West      4
## 722  2020-05-19               South West      6
## 723  2020-05-20               South West      1
## 724  2020-05-21               South West      9
## 725  2020-05-22               South West      6
## 726  2020-05-23               South West      6
## 727  2020-05-24               South West      3
## 728  2020-05-25               South West      8
## 729  2020-05-26               South West     11
## 730  2020-05-27               South West      5
## 731  2020-05-28               South West      9
## 732  2020-05-29               South West      6
## 733  2020-05-30               South West      3
## 734  2020-05-31               South West      2
## 735  2020-06-01               South West      7
## 736  2020-06-02               South West      2
## 737  2020-06-03               South West      5
## 738  2020-06-04               South West      2
## 739  2020-06-05               South West      2
## 740  2020-06-06               South West      1
## 741  2020-06-07               South West      3
## 742  2020-06-08               South West      3
## 743  2020-06-09               South West      0
## 744  2020-06-10               South West      0
## 745  2020-06-11               South West      2
## 746  2020-06-12               South West      2
## 747  2020-06-13               South West      2
## 748  2020-06-14               South West      0
## 749  2020-06-15               South West      0

1.5 Completion date

We extract the completion date from the NHS Pathways file timestamp:


database_date <- attr(x, "timestamp")
database_date
## [1] "2020-06-16"

The completion date of the NHS Pathways data is Tuesday 16 Jun 2020.

1.6 Auxiliary functions

These are functions which will be used further in the analyses.

Function to estimate the generalised R-squared as the proportion of deviance explained by a given model:


## Function to calculate R2 for Poisson model
## not adjusted for model complexity but all models have the same DF here

Rsq <- function(x) {
  1 - (x$deviance / x$null.deviance)
}

Function to extract growth rates per region as well as halving times, and the associated 95% confidence intervals:


## function to extract the coefficients, find the level of the intercept,
## reconstruct the values of r, get confidence intervals

get_r <- function(model) {
  ##  extract coefficients and conf int
  out <- data.frame(r = coef(model))  %>%
    rownames_to_column("var") %>% 
    cbind(confint(model)) %>%
    filter(!grepl("day_of_week", var)) %>% 
    filter(grepl("day", var)) %>%
    rename(lower_95 = "2.5 %",
           upper_95 = "97.5 %") %>%
    mutate(var = sub("day:", "", var))
  
  ## reconstruct values: intercept + region-coefficient
  for (i in 2:nrow(out)) {
    out[i, -1] <- out[1, -1] + out[i, -1]
  }
  
  ## find the name of the intercept, restore regions names
  out <- out %>%
    mutate(nhs_region = model$xlevels$nhs_region) %>%
    select(nhs_region, everything(), -var)
  
  ## find halving times
  halving <- log(0.5) / out[,-1] %>%
    rename(halving_t = r,
           halving_t_lower_95 = lower_95,
           halving_t_upper_95 = upper_95)
  
  ## set halving times with exclusion intervals to NA
  no_halving <- out$lower_95 < 0 & out$upper_95 > 0
  halving[no_halving, ] <- NA_real_
  
  ## return all data
  cbind(out, halving)
  
}

Functions used in the correlation analysis between NHS Pathways reports and deaths:

## Function to calculate Pearson's correlation between deaths and lagged
## reports. Note that `pearson` can be replaced with `spearman` for rank
## correlation.

getcor <- function(x, ndx) {
  return(cor(x$deaths[ndx],
             x$note_lag[ndx],
             use = "complete.obs",
             method = "pearson"))
}

## Catch if sample size throws an error
getcor2 <- possibly(getcor, otherwise = NA)

getboot <- function(x) {
  result <- boot::boot.ci(boot::boot(x, getcor2, R = 1000), 
                           type = "bca")
  return(data.frame(n = sum(!is.na(x$note_lag) & !is.na(x$deaths)),
                    r = result$t0,
                    r_low = result$bca[4],
                    r_hi = result$bca[5]))
}

Function to classify the day of the week into weekend, Monday, and the rest:


## Fn to add day of week
day_of_week <- function(df) {
  df %>% 
    dplyr::mutate(day_of_week = lubridate::wday(date, label = TRUE)) %>% 
    dplyr::mutate(day_of_week = dplyr::case_when(
      day_of_week %in% c("Sat", "Sun") ~ "weekend",
      day_of_week %in% c("Mon") ~ "monday",
      !(day_of_week %in% c("Sat", "Sun", "Mon")) ~ "rest_of_week"
    ) %>% 
      factor(levels = c("rest_of_week", "monday", "weekend")))
}

Custom color palettes, color scales, and vectors of colors:


pal <- c("#006212",
         "#ae3cab",
         "#00db90",
         "#960c00",
         "#55aaff",
         "#ff7e78",
         "#00388d")

age.pal <- viridis::viridis(3,begin = 0.1, end = 0.7)

3 Comparison with deaths time series

3.1 Outline

We want to explore the correlation between NHS Pathways reports and deaths, and assess the potential for reports to be used as an early warning system for disease resurgence.

Death data are publically available. We truncate the time series to avoid bias from reporting delay - we assume a conservative delay of three weeks.

3.2 Lagged correlation

We calculate Pearson’s correlation coefficient between deaths and NHS Pathways notifications using different lags. Confidence intervals are obtained using bootstrap. Note that results were also confirmed using Spearman’s rank correlation.

First we join the NHS Pathways and death data, and aggregate over all England:

## truncate death data for reporting delay
trunc_date <- max(dth$date_report) - delay_max

dth_trunc <- dth %>%
  rename(date = date_report) %>%
  filter(date <= trunc_date) 

## join with notification data
all_data <- x %>% 
  filter(!is.na(nhs_region)) %>%
  group_by(date, nhs_region) %>%
  summarise(count = sum(count, na.rm = T)) %>%
  ungroup %>%
  inner_join(dth_trunc,
             by = c("date","nhs_region"))

all_tot <- all_data %>%
  group_by(date) %>%
  summarise(count = sum(count, na.rm = TRUE),
            deaths = sum(deaths, na.rm = TRUE)) 

We calculate correlation with lagged NHS Pathways reports from 0 to 30 days behind deaths:


## Calculate all correlations + bootstrap CIs
lag_cor <- data.frame()
for (i in 0:30) {
  
  ## lag reports
  summary <- all_tot %>% 
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI
    getboot(.) %>%
    mutate(lag = i)

  lag_cor <- bind_rows(lag_cor, summary)
}

cor_vs_lag <- ggplot(lag_cor, aes(lag, r)) +
  theme_bw() +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi), alpha = 0.2) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_point() +
  geom_line() +
  labs(x = "Lag between NHS pathways and death data (days)",
       y = "Pearson's correlation") +
  large_txt
cor_vs_lag


l_opt <- which.max(lag_cor$r)

This analysis suggests that the best lag is 23 days. We then compare and plot the number of deaths reported against the number of NHS Pathways reports lagged by 23 days.


all_tot <- all_tot %>%
  rename(date_death = date) %>%
  mutate(note_lag = lag(count, lag_cor$lag[l_opt]),
         note_lag_c = (note_lag - mean(note_lag, na.rm = T)),
         date_note = lag(date_death,16))

lag_mod <- glm(deaths ~ note_lag, data = all_tot, family = "quasipoisson")

summary(lag_mod)
## 
## Call:
## glm(formula = deaths ~ note_lag, family = "quasipoisson", data = all_tot)
## 
## Deviance Residuals: 
##     Min       1Q   Median       3Q      Max  
## -8.9923  -2.2122  -0.2727   2.6380   4.5723  
## 
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 4.989e+00  5.254e-02   94.96   <2e-16 ***
## note_lag    1.128e-05  5.192e-07   21.73   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for quasipoisson family taken to be 10.13148)
## 
##     Null deviance: 5149.21  on 45  degrees of freedom
## Residual deviance:  460.06  on 44  degrees of freedom
##   (23 observations deleted due to missingness)
## AIC: NA
## 
## Number of Fisher Scoring iterations: 4

exp(coefficients(lag_mod))
## (Intercept)    note_lag 
##  146.777192    1.000011
exp(confint(lag_mod))
##                 2.5 %     97.5 %
## (Intercept) 132.26942 162.520656
## note_lag      1.00001   1.000012

Rsq(lag_mod)
## [1] 0.9106548

mod_fit <- as.data.frame(predict(lag_mod, type = "link", se.fit = TRUE)[1:2])

all_tot_pred <- 
  all_tot %>%
  filter(!is.na(note_lag)) %>%
  mutate(pred = mod_fit$fit,
         pred.se = mod_fit$se.fit,
         low = exp(pred - 1.96*pred.se),
         hi = exp(pred + 1.96*pred.se))


glm_fit <- all_tot_pred %>% 
    filter(!is.na(note_lag)) %>%
  ggplot(aes(x = note_lag, y = deaths)) +
  geom_point() + 
  geom_line(aes(y = exp(pred))) + 
  geom_ribbon(aes(ymin = low, ymax = hi), alpha = 0.3, col = "grey") +
  theme_bw() +
  labs(y = "Daily number of\ndeaths reported",
       x = "Daily number of NHS Pathways reports") +
  large_txt

glm_fit

4 Supplementary figures

4.1 Serial interval distribution

This is a comparison of gamma versus lognormal distribution for the serial interval used to convert r to R in our analysis. Both distributions are parameterised with mean 4.7 and standard deviation 2.9.

SI_param <- epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale, w = 0.5)

SI_distribution2 <- distcrete::distcrete("lnorm", interval = 1,
                                        meanlog = log(4.7),
                                        sdlog = log(2.9), w = 0.5)

SI_dist1 <- data.frame(x = SI_distribution$r(1e5)) 
SI_dist1 <- count(SI_dist1, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 30, 5)) +
    theme_bw()

SI_dist2 <- data.frame(x = SI_distribution2$r(1e5)) 
SI_dist2 <- count(SI_dist2, x) %>%
    ggplot() +
    geom_col(aes(x = x, y = n)) +
    labs(x = "Serial interval (days)", y = "Frequency") +
    scale_x_continuous(breaks = seq(0, 200, 20), limits = c(0, 200)) +
    theme_bw()


ggpubr::ggarrange(SI_dist1,
                  SI_dist2,
                  nrow = 1,
                  labels = "AUTO") 

4.2 Sensitivity analysis - 7 or 21 days moving window

We reproduce the window analysis with either a 7 or 21 days window for sensitivity purposes.

First with the 7 days window:

## set moving time window (1/2/3 weeks)
w <- 7

# create empty df
r_all_sliding_7days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_7days <- bind_rows(r_all_sliding_7days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_7days <- r_all_sliding_7days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
plot_R <- r_all_sliding_7days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_7days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_7days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_7 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

Then with the 21 days window:

## set moving time window (1/2/3 weeks)
w <- 21

# create empty df
r_all_sliding_21days <- NULL

## make data for model
x_model_all_moving <- x %>%
  filter(!is.na(nhs_region)) %>% 
  group_by(date, nhs_region) %>%
  summarise(n = sum(count)) 

unique_dates <- unique(x_model_all_moving$date)

for (i in 1:(length(unique_dates) - w)) {
  
  date_i <- unique_dates[i]
  
  date_i_max <- date_i + w
  
  model_data <- x_model_all_moving %>%
    filter(date >= date_i & date < date_i_max) %>%
    mutate(day = as.integer(date - date_i)) %>% 
    day_of_week()
  
  
  mod <- glm(n ~ day * nhs_region + day_of_week,
             data = model_data,
             family = 'quasipoisson')
  
  # get growth rate
  r <- get_r(mod)
  r$w_min <- date_i
  r$w_max <- date_i_max
  
  # combine all estimates
  r_all_sliding_21days <- bind_rows(r_all_sliding_21days, r)
  
}

#serial interval distribution
SI_param = epitrix::gamma_mucv2shapescale(4.7, 2.9/4.7)
SI_distribution <- distcrete::distcrete("gamma", interval = 1,
                                        shape = SI_param$shape,
                                        scale = SI_param$scale,
                                        w = 0.5)

#convert growth rates r to R0
r_all_sliding_21days <- r_all_sliding_21days %>%
  mutate(R = epitrix::r2R0(r, SI_distribution),
         R_lower_95 = epitrix::r2R0(lower_95, SI_distribution),
         R_upper_95 = epitrix::r2R0(upper_95, SI_distribution))
# plot
plot_growth <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = r)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 0, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(colour = guide_legend(title = "",override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated daily growth rate (r)") +
  scale_colour_manual(values = pal)
# plot
plot_R <-
  r_all_sliding_21days %>%
  ggplot(aes(x = w_max, y = R)) +
  geom_ribbon(aes(ymin = R_lower_95, ymax = R_upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(yintercept = 1, linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0.5,0.5, "cm")) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "",
       y = "Estimated effective reproduction\nnumber (Re)") +
  scale_colour_manual(values = pal)

R <- r_all_sliding_21days %>%
  mutate(lower_95 = R_lower_95, 
         upper_95 = R_upper_95,
         value = R,
         measure = "R",
         reference = 1)

r_R <- r_all_sliding_21days %>%
  mutate(measure = "r",
         value = r,
         reference = 0) %>%
  bind_rows(R)

r_R_21 <- r_R %>%
  ggplot(aes(x = w_max, y = value)) +
  geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = nhs_region), alpha = 0.1) +
  geom_line(aes(colour = nhs_region)) +
  geom_point(aes(colour = nhs_region)) +
  geom_hline(aes(yintercept = reference), linetype = "dashed") +
  theme_bw() +
  scale_weeks +
  theme(legend.position = "bottom",
        plot.margin = margin(0.5,1,0,0, "cm"),
        strip.background = element_blank(),
        strip.placement = "outside"
  ) +
  guides(color = guide_legend(title = "", override.aes = list(fill = NA)), fill = FALSE) +
  labs(x = "", y = "") +
  scale_colour_manual(values = pal) +
  facet_grid(rows = vars(measure),
             scales = "free_y",
             switch = "y",
             labeller = as_labeller(c(r = "Daily growth rate (r)",
                                      R = "Effective reproduction\nnumber (Re)")))

And we combine both outputs into a single plot:


ggpubr::ggarrange(r_R_7,
                  r_R_21,
                  nrow = 2,
                  labels = "AUTO",
                  common.legend = TRUE,
                  legend = "bottom") 

4.3 Correlation between NHS Pathways reports and deaths by NHS region


lag_cor_reg <- data.frame()

for (i in 0:30) {

  summary <-
    all_data %>%
    group_by(nhs_region) %>%
    mutate(note_lag = lag(count, i)) %>%
    ## calculate rank correlation and bootstrap CI for each region
    group_modify(~getboot(.x)) %>%
    mutate(lag = i)
  
  lag_cor_reg <- bind_rows(lag_cor_reg, summary)
}

cor_vs_lag_reg <- 
lag_cor_reg %>%
ggplot(aes(lag, r, col = nhs_region)) +
  geom_hline(yintercept = 0, lty = "longdash") +
  geom_ribbon(aes(ymin = r_low, ymax = r_hi, col = NULL, fill = nhs_region), alpha = 0.2) +
  geom_point() +
  geom_line() +
  facet_wrap(~nhs_region) +
  scale_color_manual(values = pal) +
  scale_fill_manual(values = pal, guide = F) +  
  theme_bw() +
  labs(x = "Lag between NHS pathways and death data (days)", y = "Pearson's correlation", col = "NHS region") +
  theme(legend.position = "bottom") +
  guides(color = guide_legend(override.aes = list(fill = NA)))

cor_vs_lag_reg

5 Export data

We save the tables created during our analysis:


if (!dir.exists("excel_tables")) {
  dir.create("excel_tables")
}


## list all tables, and loop over export
tables_to_export <- c("r_all_sliding", "lag_cor")

for (e in tables_to_export) {
  rio::export(get(e),
              file.path("excel_tables",
                        paste0(e, ".xlsx")))
}

## also export result from regression on lagged data 
rio::export(lag_mod, file.path("excel_tables", "lag_mod.rds"))

6 System information

6.1 Outline

The following information documents the system on which the document was compiled.

6.2 System

This provides information on the operating system.

Sys.info()
##                                                                                            sysname 
##                                                                                           "Darwin" 
##                                                                                            release 
##                                                                                           "19.5.0" 
##                                                                                            version 
## "Darwin Kernel Version 19.5.0: Tue May 26 20:41:44 PDT 2020; root:xnu-6153.121.2~2/RELEASE_X86_64" 
##                                                                                           nodename 
##                                                                                   "Mac-1467.local" 
##                                                                                            machine 
##                                                                                           "x86_64" 
##                                                                                              login 
##                                                                                             "root" 
##                                                                                               user 
##                                                                                           "runner" 
##                                                                                     effective_user 
##                                                                                           "runner"

6.3 R environment

This provides information on the version of R used:

R.version
##                _                           
## platform       x86_64-apple-darwin15.6.0   
## arch           x86_64                      
## os             darwin15.6.0                
## system         x86_64, darwin15.6.0        
## status                                     
## major          3                           
## minor          6.3                         
## year           2020                        
## month          02                          
## day            29                          
## svn rev        77875                       
## language       R                           
## version.string R version 3.6.3 (2020-02-29)
## nickname       Holding the Windsock

6.4 R packages

This provides information on the packages used:

sessionInfo()
## R version 3.6.3 (2020-02-29)
## Platform: x86_64-apple-darwin15.6.0 (64-bit)
## Running under: macOS Catalina 10.15.5
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggnewscale_0.4.1     ggpubr_0.3.0         lubridate_1.7.9     
##  [4] chngpt_2020.5-21     cyphr_1.1.0          DT_0.13             
##  [7] kableExtra_1.1.0     janitor_2.0.1        remotes_2.1.1       
## [10] projections_0.4.1    earlyR_0.0.1         epitrix_0.2.2       
## [13] distcrete_1.0.3      incidence_1.7.1      rio_0.5.16          
## [16] reshape2_1.4.4       rvest_0.3.5          xml2_1.3.2          
## [19] linelist_0.0.40.9000 forcats_0.5.0        stringr_1.4.0       
## [22] dplyr_1.0.0          purrr_0.3.4          readr_1.3.1         
## [25] tidyr_1.1.0          tibble_3.0.1         ggplot2_3.3.1       
## [28] tidyverse_1.3.0      here_0.1             reportfactory_0.0.5 
## 
## loaded via a namespace (and not attached):
##  [1] colorspace_1.4-1  selectr_0.4-2     ggsignif_0.6.0    ellipsis_0.3.1   
##  [5] rprojroot_1.3-2   snakecase_0.11.0  fs_1.4.1          rstudioapi_0.11  
##  [9] farver_2.0.3      fansi_0.4.1       splines_3.6.3     knitr_1.28       
## [13] jsonlite_1.6.1    broom_0.5.6       dbplyr_1.4.4      compiler_3.6.3   
## [17] httr_1.4.1        backports_1.1.7   assertthat_0.2.1  Matrix_1.2-18    
## [21] cli_2.0.2         htmltools_0.5.0   prettyunits_1.1.1 tools_3.6.3      
## [25] gtable_0.3.0      glue_1.4.1        Rcpp_1.0.4.6      carData_3.0-4    
## [29] cellranger_1.1.0  vctrs_0.3.1       nlme_3.1-144      matchmaker_0.1.1 
## [33] crosstalk_1.1.0.1 xfun_0.14         ps_1.3.3          openxlsx_4.1.5   
## [37] lifecycle_0.2.0   rstatix_0.5.0     MASS_7.3-51.5     scales_1.1.1     
## [41] hms_0.5.3         sodium_1.1        yaml_2.2.1        curl_4.3         
## [45] gridExtra_2.3     stringi_1.4.6     kyotil_2019.11-22 boot_1.3-24      
## [49] pkgbuild_1.0.8    zip_2.0.4         rlang_0.4.6       pkgconfig_2.0.3  
## [53] evaluate_0.14     lattice_0.20-38   labeling_0.3      htmlwidgets_1.5.1
## [57] cowplot_1.0.0     processx_3.4.2    tidyselect_1.1.0  plyr_1.8.6       
## [61] magrittr_1.5      R6_2.4.1          generics_0.0.2    DBI_1.1.0        
## [65] pillar_1.4.4      haven_2.3.1       foreign_0.8-75    withr_2.2.0      
## [69] mgcv_1.8-31       survival_3.1-8    abind_1.4-5       modelr_0.1.8     
## [73] crayon_1.3.4      car_3.0-8         utf8_1.1.4        rmarkdown_2.2    
## [77] viridis_0.5.1     grid_3.6.3        readxl_1.3.1      data.table_1.12.8
## [81] blob_1.2.1        callr_3.4.3       reprex_0.3.0      digest_0.6.25    
## [85] webshot_0.5.2     munsell_0.5.0     viridisLite_0.3.0